The aircraft, a Russian-made Antonov-26 twin-engine turboprob, was carrying supplies from Sanaa to Masila oilfields in the east when a technical glitch forced it to land in Hadramawt province, said General Khaled al-Kothairi, who heads a military unit tasked with protecting oil companies.
The pilot, co-pilot, and four soldiers who were on board the aircraft, are safe, he said.
But another military official said that as soon as the jet landed, armed tribesmen captured the crew and a local government official confirmed they were abducted.
The armed forces have been flying supplies to Masila oilfields five times a week over the past few months, after tribesmen blocked roads in the region to protest against the killing of one of their chiefs.
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Supporters of slain tribal chief Said Ben Habrish have vowed to avenge him by preventing authorities from repairing the pipeline that links Masila oilfield to Al-Daba port on the Gulf of Aden.
The move is aimed at depriving the cash-strapped government of Yemen, an impoverished country that relies on oil revenues from a small oil production industry, to shore up its budget.